On the bootstrap confidence intervals of the process incapability index Cpp

The process incapability index Cpp is an indicator, introduced by Greenwich and Jahr-Schaffrath, for evaluating the capability of a process. When Cpp is applied to evaluate a process, estimating the confidence interval of Cpp is important for statistical inference on the process. Calculating the confidence interval for a process index usually needs the assumption about the underlying distribution. Bootstrapping is a non-parametric, but computer intensive, estimation method. In the present paper we report the results of a simulation study on the behavior of four 95% bootstrap confidence intervals (i.e. standard bootstrap, percentile bootstrap, biased-corrected percentile bootstrap, and biased-corrected and accelerated bootstrap) for estimating Cpp when data are from a specific Burr distribution, which is used to represent various probability distributions. A detailed discussion of the simulation results is presented and some conclusions are provided.